engleski

A problem of Diophantus and its variants

One of the problems Diophantus of Alexandria was interested in was to find sets with the property that the product of any two of its distinct elements increased by one is a perfect square. There has been a lot of activity towards understanding such sets in the recent years, most notably by A. Dujella who showed that there exist at most finitely many sets consisting of five integers with the property from above, the conjecture being that there exists no such set at all. I will give an overview over some of the known results related to this problem and discuss variants of it, some of which were also already investigated by Diophantus, Fermat and Euler, and I will outline which methods are used to attack the proof of such problems.

Diophantine m-tuples

Koautori Andrej Dujella i Alan Filipin